The Fourth Basic Electric Circuit Element: MEMRISTOR Description with recent implementation.

A new two-terminal passive circuit element-called the Memristor (short for memory resistor) characterized by a relationship between the charge and the flux linkage is introduced as the fourth basic circuit element.  Another way of describing a memristor is that it is any passive two-terminal circuit elements that maintains a functional relationship between the time integral of current (called charge) and the time integral of voltage (called flux). The slope of this function is called the memristance M and is similar to variable resistance. The reason that the memristor is radically different from the other fundamental circuit elements is that, unlike them, it carries a memory of its past. When you turn off the voltage to the circuit, the memristor still remembers how much was applied before and for how long. That's an effect that can't be duplicated by any circuit combination of resistors, capacitors, and inductors, which is why the memristor qualifies as a fundamental circuit element.
 

The history of memristor starts nearly four decades ago with a nonlinear-circuit-theory pioneer Leon Chua. Examining the relationships between charge and flux in resistors, capacitors, and inductors in a 1971 paper, Chua postulated the existence of a fourth element called the memory resistor. Such a device, he figured, would provide a similar relationship between magnetic flux and charge that a resistor gives between voltage and current. In practice, that would mean it acted like a resistor whose value could vary according to the current passing through it and which would remember that value even after the current disappeared. The four circuit quantities (charge, current, voltage, and magnetic flux) can be related to each other in six ways. Two quantities are covered by basic physical laws, and three are covered by known circuit elements (resistor, capacitor, and inductor). That leaves one possible relation unaccounted for. Based on this realization, Chua proposed the memristor purely for the mathematical aesthetics of it, as a class of circuit element based on a relationship between charge and flux.

The memristor is essentially a two-terminal variable resistor, with resistance dependent upon the amount of charge q that has passed between the terminals.

Where M can be defined in terms of differential equation as,

 .

             Now, 37 years later, electronics have finally gotten small enough to reveal the secrets of that fourth element. Hewlett-Packard senior fellow Stanley Williams and his group were working on molecular electronics when they started to notice strange behavior in their devices similar as postulated by L. Chua. A solid-state device could have the characteristics of a memristor based on the behavior of nanoscale thin films. The device neither uses magnetic flux as the theoretical memristor suggested, nor do stores charge as a capacitor does, but instead achieves a resistance dependent on the history of current. The HP device is composed of a thin (50 nm) titanium dioxide film between two 5 nm thick electrodes, one Ti, the other Pt. Initially, there are two layers to the titanium dioxide film, one of which has a slight depletion of oxygen atoms. 

The oxygen vacancies act as charge carriers, meaning that the depleted layer has a much lower resistance than the non-depleted layer. When an electric field is applied, the oxygen vacancies drift (see Fast ion conductor), changing the boundary between the high-resistance and low-resistance layers. Thus the resistance of the film as a whole is dependent on how much charge has been passed through it in a particular direction, which is reversible by changing the direction of current. Since the HP device displays fast ion conduction at nanoscale, it is considered as a nanoionic device.

Spin Torque Transfer MRAM is a well-known device that exhibits memristive behavior. The resistance is dependent on the relative spin orientation between two sides of a magnetic tunnel junction. This in turn can be controlled by the spin torque induced by the current flowing through the junction. However, the length of time the current flows through the junction determines the amount of current needed. But still we are waiting for a purely memristive device.  In October 2011, the HP team announced the commercial availability of memristor technology within 18 months, as a replacement for Flash, SSD, DRAM and  SRAM.

The main reason why it is going to replace previous memory devices is that memristor never forgets. The memristor's memory has consequences: the reason computers have to be rebooted every time they are turned on is that their logic circuits are incapable of holding their bits after the power is shut off. But because a memristor can remember voltages, a memristor-driven computer would arguably never need a reboot. one could leave all his Word files and spreadsheets open, turn off your computer, and go for a break, When he comes back, turn on his computer and everything is instantly on the screen exactly the way he left it.

By redesigning certain types of circuits to include memristors same computing function can be obtained with fewer components, making the circuit itself less expensive and significantly decreasing its power consumption. In fact, combination of memristors with traditional circuit-design elements to produce a device that does computation in a non-Boolean fashion. According to R. Stanley Williams of Hewlett Packard memristor based device development team ”We won't claim that we're going to build a brain, but we want something that will compute like a brain”. They think they can abstract ”the whole synapse idea” to do essentially analog computation in an efficient manner. ”Some things that would take a digital computer forever to do, an analog computer would just breeze through”. The HP group is also looking at developing a memristor-based nonvolatile memory. A memory based on memristors could be 1000 times faster than magnetic disks and use much less power.

In short we can say that this fourth basic electric circuit element can take our today’s computing to next level making it much faster, reliable and energy efficient.